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arXiv · 1907.06395

Lifting for manifold-valued maps of bounded variation

Giacomo Canevari·Giandomenico Orlandi
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Abstract

Let $\mathcal{N}$ be a smooth, compact, connected Riemannian manifold without boundary. Let $\mathcal{E}\to\mathcal{N}$ be the Riemannian universal covering of $\mathcal{N}$. For any bounded, smooth domain $Ω\subseteq\mathbb{R}^d$ and any $u\in\mathrm{BV}(Ω, \, \mathcal{N})$, we show that $u$ has a lifting $v\in\mathrm{BV}(Ω, \, \mathcal{E})$. Our result proves a conjecture by Bethuel and Chiron.

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Giacomo Canevari, Giandomenico Orlandi. 2019-11-30. Lifting for manifold-valued maps of bounded variation. https://arxiv.org/abs/1907.06395

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